From time to time, consumers have a need for wiping products, such as tissue or wet wipes, when they are away from home. Existing commercial products, which consist of a small roll of toilet paper within a rigid thermoformed plastic dispenser, generally meet the need for providing a relatively portable source of small amount of toilet paper. To access the roll of toilet paper, the user opens the dispenser to expose the roll, grasps the available leading edge of the roll and removes the desired amount of toilet paper. However, such products require handling or touching of the small roll, which can be unsanitary. Also, the rigid plastic container can be a bit bulky due to its size and rigidity, which is unsuitable for storage in some pockets and also takes up a fair amount of space if placed in one's purse. Therefore there is a need for a portable wiping product which provides a relatively small amount of tissue or wet wipes for a limited number of use occasions and which can be more easily carried in one's pocket or purse.